adolc_poly.cpp

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Adolc Speed: Second Derivative of a Polynomial

Specifications

See link_poly .

Implementation

// suppress conversion warnings before other includes
# include <cppad/wno_conversion.hpp>
//
# include <vector>
# include <adolc/adolc.h>

# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/poly.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/utility/thread_alloc.hpp>
# include "adolc_alloc_mat.hpp"

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_poly(
   size_t                     size     ,
   size_t                     repeat   ,
   CppAD::vector<double>     &a        ,  // coefficients of polynomial
   CppAD::vector<double>     &z        ,  // polynomial argument value
   CppAD::vector<double>     &ddp      )  // second derivative w.r.t z
{
   if( global_option["atomic"] )
      return false;
   if( global_option["memory"] || global_option["optimize"] )
      return false;
   // -----------------------------------------------------
   // setup
   size_t i;
   short tag  = 0;  // tape identifier
   int   keep = 0;  // do not keep forward mode results in buffer
   int   m    = 1;  // number of dependent variables
   int   n    = 1;  // number of independent variables
   int   d    = 2;  // highest derivative degree
   double f;        // function value

   // set up for thread_alloc memory allocator (fast and checks for leaks)
   using CppAD::thread_alloc; // the allocator
   size_t capacity;           // capacity of an allocation

   // choose a vector of polynomial coefficients
   CppAD::uniform_01(size, a);

   // AD copy of the polynomial coefficients
   std::vector<adouble> A(size);
   for(i = 0; i < size; i++)
      A[i] = a[i];

   // domain and range space AD values
   adouble Z, P;

   // allocate arguments to hos_forward
   double* x0 = thread_alloc::create_array<double>(size_t(n), capacity);
   double* y0 = thread_alloc::create_array<double>(size_t(m), capacity);
   double** x = adolc_alloc_mat(size_t(n), size_t(d));
   double** y = adolc_alloc_mat(size_t(m), size_t(d));

   // Taylor coefficient for argument
   x[0][0] = 1.;  // first order
   x[0][1] = 0.;  // second order

   // ----------------------------------------------------------------------
   if( ! global_option["onetape"] ) while(repeat--)
   {  // choose an argument value
      CppAD::uniform_01(1, z);

      // declare independent variables
      trace_on(tag, keep);
      Z <<= z[0];

      // AD computation of the function value
      P = CppAD::Poly(0, A, Z);

      // create function object f : Z -> P
      P >>= f;
      trace_off();

      // set the argument value
      x0[0] = z[0];

      // evaluate the polynomial at the new argument value
      hos_forward(tag, m, n, d, keep, x0, x, y0, y);

      // second derivative is twice second order Taylor coef
      ddp[0] = 2. * y[0][1];
   }
   else
   {
      // choose an argument value
      CppAD::uniform_01(1, z);

      // declare independent variables
      trace_on(tag, keep);
      Z <<= z[0];

      // AD computation of the function value
      P = CppAD::Poly(0, A, Z);

      // create function object f : Z -> P
      P >>= f;
      trace_off();

      while(repeat--)
      {  // get the next argument value
         CppAD::uniform_01(1, z);
         x0[0] = z[0];

         // evaluate the polynomial at the new argument value
         hos_forward(tag, m, n, d, keep, x0, x, y0, y);

         // second derivative is twice second order Taylor coef
         ddp[0] = 2. * y[0][1];
      }
   }
   // ------------------------------------------------------
   // tear down
   adolc_free_mat(x);
   adolc_free_mat(y);
   thread_alloc::delete_array(x0);
   thread_alloc::delete_array(y0);

   return true;
}